The folding of DNA in nucleosomes is accompanied by the lateral displacements of adjacent base pairs, which are usually ignored. We have found, however, that the shear deformation, called Slide, plays a much more important role in DNA folding than was previously imagined. First, the lateral Slide deformations observed at sites of local anisotropic bending of DNA define its superhelical trajectory in chromatin. (Note that the nucleosomal DNA twisting remains close, on average, to that in solution. In other words, the 'real' DNA wrapping around the histone core is inconsistent with the conventional model of superhelical DNA, which links changes in superhelical pitch to DNA twisting.) Second, the computed cost of deforming DNA on the nucleosome is sequence specific: in optimally positioned sequences the most easily deformed base-pair steps (CA:TG and TA) occur at sites of large positive Slide and negative Roll (where the DNA bends, or kinks, into the minor groove). Here, we incorporate all the degrees of freedom of 'real' DNA, thereby going beyond the limits of the conventional model - the latter ignores the lateral Slide displacements of base pairs, and as a result, fails to account for the preferable positioning of the TA steps. Indeed, only after lateral Slide displacements are considered, are we able to account for the sequence-specific positioning of nucleosomes in vitro. Our findings agree with the results of in vitro sequence selection (SELEX) experiments (e.g., the most stable nucleosomal fragment 601 detected by Jon Widom). The successful prediction of nucleosome positioning for sequences of various GC-content demonstrates the potential advantage of our structural analysis, based on calculations of the DNA deformation energy. Next, we will apply our method to the analysis of GC-rich mammalian promoters. In addition to DNA folding in nucleosomes, the shearing deformations are implicated in the sequence-specific recognition of DNA by transcription factors, such as the tumor suppressor protein p53. The DNA bending, twisting and sliding (first, predicted by us and then observed in solution upon p53 binding) are entirely consistent with the 'Kink-and-Slide' conformation described above. Therefore, structural organization of a p53 binding site in chromatin can regulate its affinity to p53 - for example, exposure of the DNA site on nucleosomal surface would facilitate the p53 binding to the response elements regulating cell cycle arrest genes (p21, GADD45, etc.). Our results indicate that there is a complex interplay between the structural codes encrypted in eukaryotic genomes - one code for DNA packaging in chromatin, and the other code for DNA recognition by regulatory proteins. Rather than being mutually exclusive (as was assumed earlier), the two codes appear to be consistent with each other. At least in some cases, such as p53 and NF-&#954;B, the DNA wrapping in nucleosomes can facilitate binding of the transcription factor to its cognate sequence, provided that the latter is properly exposed in chromatin.